Journal of the ACM最新文献

Tree search algorithms, such as branch-and-bound, are the most widely used tools for solving combinatorial and non-convex problems. For example, they are the foremost method for solving (mixed) integer programs and constraint satisfaction problems. Tree search algorithms come with a variety of tunable parameters that are notoriously challenging to tune by hand. A growing body of research has demonstrated the power of using a data-driven approach to automatically optimize the parameters of tree search algorithms. These techniques use a training set of integer programs sampled from an application-specific instance distribution to find a parameter setting that has strong average performance over the training set. However, with too few samples, a parameter setting may have strong average performance on the training set but poor expected performance on future integer programs from the same application. Our main contribution is to provide the first sample complexity guarantees for tree search parameter tuning. These guarantees bound the number of samples sufficient to ensure that the average performance of tree search over the samples nearly matches its future expected performance on the unknown instance distribution. In particular, the parameters we analyze weight scoring rules used for variable selection. Proving these guarantees is challenging because tree size is a volatile function of these parameters: we prove that for any discretization (uniform or not) of the parameter space, there exists a distribution over integer programs such that every parameter setting in the discretization results in a tree with exponential expected size, yet there exist parameter settings between the discretized points that result in trees of constant size. In addition, we provide data-dependent guarantees that depend on the volatility of these tree-size functions: our guarantees improve if the tree-size functions can be well-approximated by simpler functions. Finally, via experiments, we illustrate that learning an optimal weighting of scoring rules reduces tree size.

A new Las Vegas algorithm is presented for the composition of two polynomials modulo a third one, over an arbitrary field. When the degrees of these polynomials are bounded by n, the algorithm uses On^1.43 field operations, breaking through the 3/2 barrier in the exponent for the first time. The previous fastest algebraic algorithms, due to Brent and Kung in 1978, require On^1.63 field operations in general, and n^{3/2 + o(1)} field operations in the special case of power series over a field of large enough characteristic. If cubic-time matrix multiplication is used, the new algorithm runs in n^{5/3 + o(1)} operations, while previous ones run in On² operations.

Our approach relies on the computation of a matrix of algebraic relations that is typically of small size. Randomization is used to reduce arbitrary input to this favorable situation.

In the setting where participants are asked multiple similar possibly subjective multi-choice questions (e.g. Do you like Panda Express? Y/N; do you like Chick-fil-A? Y/N), a series of peer prediction mechanisms have been designed to incentivize honest reports and some of them achieve dominantly truthfulness: truth-telling is a dominant strategy and strictly dominate other “non-permutation strategy” with some mild conditions. However, those mechanisms require the participants to perform an infinite number of tasks. When the participants perform a finite number of tasks, these mechanisms only achieve approximated dominant truthfulness. The existence of a dominantly truthful multi-task peer prediction mechanism that only requires a finite number of tasks remains to be an open question that may have a negative result, even with full prior knowledge.

This paper answers this open question by proposing a family of mechanisms, VMI-Mechanisms, that are dominantly truthful with a finite number of tasks. A special case of this family, DMI-Mechanism, only requires ≥ 2C tasks where C is the number of choices for each question (C = 2 for binary-choice questions). The implementation of these mechanisms does not require any prior knowledge (detail-free) and only requires ≥ 2 participants. To the best of our knowledge, any mechanism of the family is the first dominantly truthful peer prediction mechanism that works for a finite number of tasks.

The core of these new mechanisms is a new family of information-monotone information measures: volume mutual information (VMI). VMI is based on a simple geometric information measure design method, the volume method. The volume method measures the informativeness of an object by “counting” the number of objects that are less informative than it. In other words, the more objects that the object of interest dominates, the more informative it is considered to be.

Finally, in the setting where agents need to invest efforts to obtain their private signals, we show how to select the mechanism to optimally incentivize efforts among a proper set of VMI-Mechanisms.

We study equi-join computation in the massively parallel computation (MPC) model. Currently, a main open question under this topic is whether it is possible to design an algorithm that can process any join with load (O(N {rm {polylog}} N / p^{1/rho ^*}) ) — measured in the number of words communicated per machine — where N is the total number of tuples in the input relations, ρ^* is the join’s fractional edge covering number, and p is the number of machines. We settle the question in the negative for the class of tuple-based algorithms (all the known MPC join algorithms fall in this class) by proving the existence of a join query with ρ^* = 2 that requires a load of Ω(N/p^1/3) to evaluate. Our lower bound provides solid evidence that the “AGM bound” alone is not sufficient for characterizing the hardness of join evaluation in MPC (a phenomenon that does not exist in RAM). The hard join instance identified in our argument is cyclic, which leaves the question of whether (O(N {rm {polylog}} N / p^{1/rho ^*}) ) is still possible for acyclic joins. We answer this question in the affirmative by showing that any acyclic join can be evaluated with load (O(N / p^{1/rho ^*}) ), which is asymptotically optimal (there are no polylogarithmic factors in our bound). The separation between cyclic and acyclic joins is yet another phenomenon that is absent in RAM. Our algorithm owes to the discovery of a new mathematical structure — we call “canonical edge cover” — of acyclic hypergraphs, which has numerous non-trivial properties and makes an elegant addition to database theory.